1
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2

The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_{1}$ to $R_{8}$, and two ideal batteries with voltages $\varepsilon_{1}=12 \mathrm{~V}$ and $\varepsilon_{2}=6 \mathrm{~V}$.

Which of the following statement(s) is(are) correct?

A
The magnitude of current flowing through $R_{1}$ is $7.2 \mathrm{~A}$.
B
The magnitude of current flowing through $R_{2}$ is $1.2 \mathrm{~A}$.
C
The magnitude of current flowing through $R_{3}$ is $4.8 \mathrm{~A}$.
D
The magnitude of current flowing through $R_{5}$ is $2.4 \mathrm{~A}$.
2
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2

An ideal gas of density $\rho=0.2 \mathrm{~kg} \mathrm{~m}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=$ $0.8 \mathrm{~kg} \mathrm{~s}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_{1}=0.1 \mathrm{~m}^{2}$ and the upper end is $A_{2}=0.4 \mathrm{~m}^{2}$. The pressure and the temperature of the gas at the lower end are $600 \mathrm{~Pa}$ and $300 \mathrm{~K}$, respectively, while its temperature at the upper end is $150 \mathrm{~K}$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ and the ratio of specific heats of the gas $\gamma=2$. Ignore atmospheric pressure.

Which of the following statement(s) is(are) correct?

A
The pressure of the gas at the upper end of the chimney is $300 \mathrm{~Pa}$.
B
The velocity of the gas at the lower end of the chimney is $40 \mathrm{~m} \mathrm{~s}^{-1}$ and at the upper end is $20 \mathrm{~ms}^{-1}$.
C
The height of the chimney is $590 \mathrm{~m}$.
D
The density of the gas at the upper end is $0.05 \mathrm{~kg} \mathrm{~m}^{-3}$.
3
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2

Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l>0$ from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.

Which of the following statement(s) is(are) correct?

A
The ray of light will come out for $\theta=30^{\circ}$, for $0< l < L$.
B
There is an angle for $l=\frac{L}{2}$ at which the ray of light will come out after two reflections.
C
The ray of light will NEVER come out for $\theta=60^{\circ}$, and $l=\frac{L}{3}$.
D
The ray of light will come out for $\theta=60^{\circ}$, and $0 < l < \frac{L}{2}$ after six reflections.
4
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2

Six charges are placed around a regular hexagon of side length $a$ as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center 0 of the hexagon and is bisected by the side.

Which of the following statement(s) is(are) correct in SI units?

A
When $x=q$, the magnitude of the electric field at 0 is zero.
B
When $x=-q$, the magnitude of the electric field at 0 is $\frac{q}{6 \pi \epsilon_{o} a^{2}}$.
C
When $x=2 q$, the potential at 0 is $\frac{7 q}{4 \sqrt{3} \pi \epsilon_{o} a}$.
D
When $x=-3 q$, the potential at 0 is $-\frac{3 q}{4 \sqrt{3} \pi \epsilon_{o} a}$.
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